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%I #6 Mar 13 2015 00:57:06
%S 1,8,57,308,1989,13161,94939
%N Number of balanced primes (A090403) less than 10^n.
%C The average number of balanced primes, p_n, seems to reach a maximum at the 85th prime, 439, of 32 balanced primes.
%C A096711(n)/A006880(n) begins 25%, 32%, 33.93%, 25.06%, 20.74%
%t f[n_] := f[n] = Block[{c = 0, k = 1, p = Prime[n], s = Plus @@ Table[Prime[i], {i, n - 1, n + 1}]}, While[k != n - 1, If[s == (2k + 1)p, Return[1]]; k++; s = s + Prime[n - k] + Prime[n + k]]; 0]; f[1] = 0; Do[ f[n], {n, 10000}]; s = Prime[ Select[ Range[ 10000], f[ # ] == 1 &]]; Table[ Length[ Select[s, # < 10^n &]], {n, 5}]
%Y Cf. A090403.
%K nonn
%O 1,2
%A _Robert G. Wilson v_, Jul 03 2004
%E a(6)-a(7) from _Donovan Johnson_, Apr 09 2010
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